Bayesian calibration and Bayesian model comparison of a stand level dynamic growth model for Sitka spruce and Scots pine

Abstract

Growth models continue to be of importance in modern multi-functional forestry to provide forecasts. Bayesian calibrations allow both model structure and parameters to be assessed simultaneously in a probabilistic framework, providing a model with which forecasts and their uncertainty can be better understood and quantified using posterior probability distributions. A Bayesian calibration of a stand-level dynamic growth (SLeDG) model is carried out for both Sitka spruce and Scots pine in the UK for the first time. The calibration used the differential evolution Markov-Chain method to reduce the required number of iterations for inference. Two different model structures were considered for estimating local stand productivity: one using the measured height-age relationship, and one using estimated site yield class. The height-age relationship was shown to be more probable for both species in a Bayesian model comparison (total model probability$=$0.64 and 0.58 for Sitka spruce and Scots pine, respectively), although metrics of model performance were similar for both model structures ($R2 \geq 0.88$ in all variables). A complete calibration (using all data) of the more probable model structure was then completed, and excellent model fit was observed ($R2 >0.95$ for all variables in both species). Example forecasts using the output from the calibration were demonstrated, and are compatible with existing yield tables for both species. This method could be applied to other species or other model structures in the future.