Evaluation of uncertainties in N 2 O and NO fluxes from agricultural soil using a hierarchical Bayesian model

Agricultural soil is the major source of nitrous oxide (N 2 O) and nitric oxide (NO). However, N 2 O and NO fluxes from the soil show high spatial and temporal variability. Therefore, traditional statistical tools are insufficient for evaluating the strength of the emissions and determining the environmental and management factors affecting these fluxes. To compensate for the inherent variability of N oxide fluxes in situ, we proposed the application of a hierarchical Bayesian (HB) model based on a simple semi‐mechanistic model with a lognormal probability distribution. We applied the HB model to the daily N 2 O and NO fluxes from an Andosol soil field to which a chemical N fertilizer was applied. In addition, we evaluated the responses of these fluxes to environmental factors and N application. The posterior inference revealed various sensitivities to the soil temperature and water‐filled pore space (WFPS) among the N oxide gas fluxes. The N 2 O flux showed a higher temperature dependency compared with the NO flux. The estimated optimum WFPS of the NO flux (54.1% with credible interval (CI) 95%, from 47.1% to 79.4%) was lower than that of the N 2 O flux (75.8% with CI 95%, from 54.1% to 98.3%) in this soil sample. Although control plots without N fertilizer application are usually required to calculate the fertilizer‐induced emission factor (EF), our HB model could estimate EFs and their uncertainties using posterior simulations (for N 2 O 0.077% with CI 95% high probability density, from 0.056% to 0.191%; for NO 0.875% with CI 95% high probability density, from 0.552% to 2.05%). Our HB model can be easily applied to the observations of the N 2 O and NO fluxes because it requires only several explanatory variables and can be used to evaluate the flux uncertainties and responses of the nonlinear N oxide fluxes to environmental factors.