Bayesian calibration of simple forest models with multiplicative mathematical structure: A case study with two Light Use Efficiency models in an alpine forest

Abstract Forest models are increasingly being used to study ecosystem functioning, through simulation of carbon fluxes and productivity in different biomes and plant functional types all over the world. Several forest models based on the concept of Light Use Efficiency (LUE) rely mostly on a simplified mathematical structure and empirical parameters, require little amount of data to be run, and their computations are usually fast. However, possible calibration issues must be investigated in order to ensure reliable results. Here we addressed the important issue of delayed convergence when calibrating LUE models, characterized by a multiplicative structure, with a Bayesian approach. We tested two models (Prelued and the Horn and Schulz (2011a) model), applying three Markov Chain Monte Carlo-based algorithms with different number of iterations, and different sets of prior parameter distributions with increasing information content. The results showed that recently proposed algorithms for adaptive calibration did not confer a clear advantage over the Metropolis–Hastings Random Walk algorithm for the forest models used here, and that a high number of iterations is required to stabilize in the convergence region. This can be partly explained by the multiplicative mathematical structure of the models, with high correlations between parameters, and by the use of empirical parameters with neither ecological nor physiological meaning. The information content of the prior distributions of the parameters did not play a major role in reaching convergence with a lower number of iterations. We conclude that there is a need for a more careful approach to calibration to solve potential problems when applying models characterized by a multiplicative mathematical structure. Moreover, the calibration proved time consuming and mathematically difficult, so advantages of using a computationally fast and user-friendly model were lost due to the calibration process needed to obtain reliable results.

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