Bayesian inference and predictive performance of soil respiration models in the presence of model discrepancy

Abstract

Abstract. Bayesian inference of microbial soil respiration models is often based on the\nassumptions that the residuals are independent (i.e., no temporal or spatial\ncorrelation), identically distributed (i.e., Gaussian noise), and have\nconstant variance (i.e., homoscedastic). In the presence of model\ndiscrepancy, as no model is perfect, this study shows that these assumptions\nare generally invalid in soil respiration modeling such that residuals have\nhigh temporal correlation, an increasing variance with increasing magnitude\nof CO2 efflux, and non-Gaussian distribution. Relaxing these three\nassumptions stepwise results in eight data models. Data models are the basis\nof formulating likelihood functions of Bayesian inference. This study\npresents a systematic and comprehensive investigation of the impacts of data\nmodel selection on Bayesian inference and predictive performance. We use\nthree mechanistic soil respiration models with different levels of model\nfidelity (i.e., model discrepancy) with respect to the number of carbon pools\nand the explicit representations of soil moisture controls on carbon\ndegradation; therefore, we have different levels of model complexity with\nrespect to the number of model parameters. The study shows that data models\nhave substantial impacts on Bayesian inference and predictive performance of\nthe soil respiration models such that the following points are true: (i)\xa0the\nlevel of complexity of the best model is generally justified by the\ncross-validation results for different data models; (ii)\xa0not accounting for\nheteroscedasticity and autocorrelation might not necessarily result in biased\nparameter estimates or predictions, but will definitely underestimate\nuncertainty; (iii)\xa0using a non-Gaussian data model improves the parameter\nestimates and the predictive performance; and (iv)\xa0accounting for autocorrelation\nonly or joint inversion of correlation and heteroscedasticity can be problematic\nand requires special treatment. Although the conclusions of this study are empirical, the analysis may provide insights\nfor selecting appropriate data models for soil respiration modeling.