Model complexity and data worth: An assessment of changes in the global carbon budget

Abstract

Although an increase in atmospheric CO 2 has been well documented by long-term measurements, there remain substantial uncertainties in the sources of atmospheric CO 2 inputs. While considerable effort has been devoted to the measurement of carbon fluxes and to the development of models to simulate the fluxes between compartments, little effort has been devoted toward assessing the uncertainties in model predictions. Using hypothesis testing methods applied to a state-space formulation of carbon flux models of varying levels of complexity, it is possible to determine the power of tests to discriminate between model formulations of varying complexity, and to determine the worth of data for such discrimination given varying levels of measurement error. A series of Monte Carlo tests were performed, using as the generating model a nonlinear global carbon cycle model from which multiple 100-year global carbon scenarios were produced. The ability of a likelihood ratio test to discriminate between three alternate linear models was then evaluated. Except when the measurement error was quite low, even a simple four-compartment linearized model could not be discriminated from the true nonlinear model. Data worth was evaluated by assessing the change in the length of the time required to identify a change in atmospheric CO 2 for a given change in measurement error for each of the state variables. The results showed that detection times decreased most rapidly for reductions in error of measurement of the living terrestrial biota and atmospheric compartments. The effect of measurement error in the soil compartment was of intermediate significance, while the role of the deep and intermediate ocean compartments was slight, and that of the surface ocean layer negligible. Insofar as the reduction of measurement errors, in the context considered here, implies large-scale research programs, these results should help to prioritize resource allocation for long-term CO 2 assessments.