Uncertainty in model parameters and regional carbon fluxes: A model-data fusion approach

Models have been widely used to estimate carbon fluxes at regional scales, and the uncertainty of modeled fluxes, however, has rarely been quantified and remains a challenge. A quantitative uncertainty assessment of regional flux estimates is essential for better understanding of terrestrial carbon dynamics and informing carbon and climate decision-making. We use a simple ecosystem model, eddy covariance (EC) flux observations, and a model-data fusion approach to assess the uncertainty of regional carbon flux estimates for the Upper Midwest region of northern Wisconsin and Michigan, USA. We combine net ecosystem exchange (NEE) observations and an adaptive Markov chain Monte Carlo (MCMC) approach to quantify the parameter uncertainty of the Diagnostic Carbon Flux Model (DCFM). Our MCMC approach eliminates the need for an initial equilibration or “burn-in” phase of the random walk, and also improves the performance of the algorithm for parameter optimization. For each plant functional type (PFT), we use NEE observations from multiple EC sites to estimate parameters, and the resulting parameter estimates are more representative of the PFT than estimates based on observations from a single site. A probability density function (PDF) is generated for each parameter, and the spread of the PDF provides an estimate of parameter uncertainty. We then apply the model with parameter PDFs to estimate NEE for each grid cell across our study region, and propagate the parameter uncertainty through simulations to produce probabilistic flux estimates. Over the period from 2001 to 2007, the mean annual NEE of the region was estimated to be −30.0 Tg C yr−1, and the associated uncertainty as measured by standard deviation was ± 7.6 Tg C yr−1. Uncertainty in parameters can lead to a large uncertainty to estimates of regional carbon fluxes, and our model-data approach can provide uncertainty bounds to regional carbon fluxes. Future research is needed to apply our approach to more complex ecosystem models, assess the usefulness, validity, and alternatives of the PFT and vegetation type concepts, and to fully quantify the uncertainty of regional carbon fluxes by incorporating other sources of uncertainty.