Abstract
Abstract. Calibration of terrestrial ecosystem models is important but challenging. Bayesian inference implemented by Markov chain Monte Carlo (MCMC) sampling provides a comprehensive framework to estimate model parameters and associated uncertainties using their posterior distributions. The effectiveness and efficiency of the method strongly depend on the MCMC algorithm used. In this work, a differential evolution adaptive Metropolis (DREAM) algorithm is used to estimate posterior distributions of 21 parameters for the data assimilation linked ecosystem carbon (DALEC) model using 14 years of daily net ecosystem exchange data collected at the Harvard Forest Environmental Measurement Site eddy-flux tower. The calibration of DREAM results in a better model fit and predictive performance compared to the popular adaptive Metropolis (AM) scheme. Moreover, DREAM indicates that two parameters controlling autumn phenology have multiple modes in their posterior distributions while AM only identifies one mode. The application suggests that DREAM is very suitable to calibrate complex terrestrial ecosystem models, where the uncertain parameter size is usually large and existence of local optima is always a concern. In addition, this effort justifies the assumptions of the error model used in Bayesian calibration according to the residual analysis. The result indicates that a heteroscedastic, correlated, Gaussian error model is appropriate for the problem, and the consequent constructed likelihood function can alleviate the underestimation of parameter uncertainty that is usually caused by using uncorrelated error models.
Highlights
Prediction of future climate heavily depends on accurate predictions of the concentration of carbon dioxide (CO2) in the atmosphere
Since multimodality is a potential feature of complex problems including terrestrial ecosystem models (Stead et al, 2005; Thibault et al, 2011), it is important to understand the strategies of adaptive Metropolis (AM) and differential evolution adaptive Metropolis (DREAM) and to investigate their capabilities in sampling the multimodal distributions
Previous studies based on Markov chain Monte Carlo (MCMC) methods that used Gaussian proposals have not reported multimodality in the marginal posterior probability density functions (PPDFs) of the model parameters, so it is important to know whether the parameters have multimodality; if the multimodality exists, we assess whether or not DREAM can identify the multiple modes and improve the calibration results and the predictive performance
Summary
Prediction of future climate heavily depends on accurate predictions of the concentration of carbon dioxide (CO2) in the atmosphere. The single-chain and Gaussian-proposal MCMC approaches have limitations in sufficiently exploring the full parameter space and share slow convergence in sampling the non-Gaussian-shaped PPDFs and may end up with a local optimum with inaccurate uncertainty representation of the parameters This poses a question on whether the AM and the widely used MCMC algorithms with Gaussian proposal generate a representing sample of the posterior distribution of the underlying model parameters. It uses the differential evolution optimization method to generate the candidate samples from the collection of chains (Price et al, 2005) This feature of DREAM eliminates the problem of initializing the proposal covariance matrix and enables efficient handling of complex distributions with strong correlations.
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