Bayesian analysis of a carbon cycle model: Implications for parameter estimation, model selection, and simulation of beetle-caused forest mortality

Background/Question/Methods

In recent decades, forest mortality due to bark beetle infestation in conifer forests of western North America has reached epidemic levels, which may have profound effects on net primary production, heterotrophic respiration (R_h), and hence the net carbon flux between forest and atmosphere (NEE). The response of R_h to changing climate and disturbance is a major concern as it is a major factor controlling the carbon balance of forests, yet remains poorly constrained and weakly represented in ecosystem models. Beetles may alter respiration through both a reduction in autotrophic respiration (R_a) caused by tree mortality and an increase in R_hfrom increasing substrate. Bayesian analysis allows for testing of prior assumptions or measurements of model parameters given an observed set of data, and also allows for comparison between different models and model structures. We hypothesized that uncertainty in measurements of NEE and ecosystem respiration allow for many acceptable models and model forms.  However, we also hypothesized that not all models would be statistically equivalent when evaluated in a Bayesian framework nor would all estimated parameters agree with prior distributions. We implemented the most probable model to simulate a bark beetle infestation over the period 2005-2011 in a sub-alpine conifer forest at the Glacier Lakes Ecosystem Experiment Site (GLEES) in southeast Wyoming. Model outputs were compared to both eddy-covariance data and measurements from respiration chambers.

Results/Conclusions

Bayesian analysis of the various configurations of respiration sub-models within a larger ecosystem model suggested that some model formulations were significantly better when measured by deviance information criteria (DIC, a Bayesian measure of model fit or adequacy) and standard error in NEE estimation at the GLEES study site.  Specifically, autotrophic respiration models that included nitrogen concentration in respiring tissue had the lowest (best) DIC while producing posterior parameter intervals (95%) that contained the prior values.  Within heterotrophic respiration models, the recently proposed Dual-Arrhenius Michaelis Menten (DAMM) model (Davidson et al. 2012) had the lowest DIC compared to standard empirical formulations of R_h based on temperature and moisture. The 7-year simulation was run at a 30-minute time step and covered the pre- to post-beetle infestation period. Simulated NEE ranged from 10 to -19 μmol CO₂ m^-2 s^-1, and standard error in predicted half-hourly NEE was <3 μmol CO₂ m^-2 s^-1. Difference between simulated and observed NEE did not differ between phases of beetle attack.