A Bayesian framework for model calibration, comparison and analysis: Application to four models for the biogeochemistry of a Norway spruce forest

► Four models of forest biogeochemistry were analysed in a Bayesian framework. ► The framework comprises model calibration, model comparison, analysis of model–data mismatch. ► We used data on soil water content and emissions of CO2, N2O and NO in a Norway spruce forest. ► Uncertainties about measurement error, model structure and parameterisation were quantified. ► We found high probabilities of systematic error in CO2 measurements and in model structure. Four different parameter-rich process-based models of forest biogeochemistry were analysed in a Bayesian framework consisting of three operations: (1) Model calibration, (2) Model comparison, (3) Analysis of model–data mismatch. Data were available for four output variables common to the models: soil water content and emissions of N2O, NO and CO2. All datasets consisted of time series of daily measurements. Monthly averages and quantiles of the annual frequency distributions of daily emission rates were calculated for comparison with equivalent model outputs. This use of the data at model-appropriate temporal scale, together with the choice of heavy-tailed likelihood functions that accounted for data uncertainty through random and systematic errors, helped prevent asymptotic collapse of the parameter distributions in the calibration. Model behaviour and how it was affected by calibration was analysed by quantifying the normalised RMSE and r2 for the different output variables, and by decomposition of the MSE into contributions from bias, phase shift and variance error. The simplest model, BASFOR, seemed to underestimate the temporal variance of nitrogenous emissions even after calibration. The model of intermediate complexity, DAYCENT, simulated the time series well but with large phase shift. COUP and MoBiLE-DNDC were able to remove most bias through calibration. The Bayesian framework was shown to be effective in improving the parameterisation of the models, quantifying the uncertainties in parameters and outputs, and evaluating the different models. The analysis showed that there remain patterns in the data – in particular infrequent events of very high nitrogenous emission rate – that are unexplained by any of the selected forest models and that this is unlikely to be due to incorrect model parameterisation.