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. Bayesian inference of microbial soil respiration models is often based on theassumptions that the residuals are independent (i.e., no temporal or spatialcorrelation), identically distributed (i.e., Gaussian noise), and haveconstant variance (i.e., homoscedastic). In the presence of modeldiscrepancy, as no model is perfect, this study shows that these assumptionsare generally invalid in soil respiration modeling such that residuals havehigh temporal correlation, an increasing variance with increasing magnitudeof CO2 efflux, and non-Gaussian distribution. Relaxing these threeassumptions stepwise results in eight data models. Data models are the basisof formulating likelihood functions of Bayesian inference. This studypresents a systematic and comprehensive investigation of the impacts of datamodel selection on Bayesian inference and predictive performance. We usethree mechanistic soil respiration models with different levels of modelfidelity (i.e., model discrepancy) with respect to the number of carbon poolsand the explicit representations of soil moisture controls on carbondegradation; therefore, we have different levels of model complexity withrespect to the number of model parameters. The study shows that data modelshave substantial impacts on Bayesian inference and predictive performance ofthe soil respiration models such that the following points are true: (i) thelevel of complexity of the best model is generally justified by thecross-validation results for different data models; (ii) not accounting forheteroscedasticity and autocorrelation might not necessarily result in biasedparameter estimates or predictions, but will definitely underestimateuncertainty; (iii) using a non-Gaussian data model improves the parameterestimates and the predictive performance; and (iv) accounting for autocorrelationonly or joint inversion of correlation and heteroscedasticity can be problematicand requires special treatment. Although the conclusions of this study are empirical, the analysis may provide insightsfor selecting appropriate data models for soil respiration modeling.

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