A Bayesian inversion framework to evaluate parameter and predictive inference of a simple soil respiration model in a cool-temperate forest in western Japan

Careful modelling of soil carbon sequestration is essential to evaluate future terrestrial feedback to the earth climate system through atmosphere–surface carbon exchange. Few studies have evaluated, in bio- and geo-applications, parameter and predictive uncertainty of soil respiration models by considering the difference between observations and model predictions; i.e. residual error, which is assumed neither to be independent nor to be described by a normal (i.e. Gaussian) probability distribution with a mean of zero and constant variance. In this paper, we use 2-year observations of soil carbon flux from 2017 to 2018 (hereafter referred to as ‘long-term simulation’) obtained with two open-top chambers to estimate parameter and predictive uncertainty of a simple soil respiration model based on Bayesian statistics in a cool-temperate forest in western Japan. We also use a Gaussian innovative residual error model in which a generalised likelihood uncertainty estimation that accounts for correlated, heteroscedastic, non-normally distributed (i.e. non-Gaussian) residual error flexibly handles statistics varying in skewness and kurtosis. Results show that the effects of correlation and heteroscedasticity were eliminated adequately. Additionally, the posterior distribution of the residuals had a pattern intermediate to those of Gaussian and Laplacian (or double-exponential) distributions. Consequently, the predicted soil respiration rate, and range of uncertainty therein, well-matched the observational data. Furthermore, we compare results of parameter and predictive inference of the soil respiration model from the long-term simulation with those constrained of short-term simulations (i.e. 4-month subsets of the 2-year dataset) to determine the extent to which the approach used affects the estimation of parameter and predictive uncertainty. No significant difference in parameter estimates was found between the long-term simulation versus any of the short-term simulations, whereas short-term simulation analysis of the uncertainty at 50 %—i.e. between the lower (25 %) and upper (75 %) quartiles of the probability range—indicated distinctive variations in model parameters in summer when more vigorous activity of trees and organisms promotes carbon cycling between the atmosphere and ecosystem. Overall we demonstrate that the Bayesian inversion approach is useful as a means by which to evaluate effectively parameter and predictive uncertainty of a soil respiration model with precise representation of residual errors.