Unraveling nitrous oxide in free-stall dairy barns: A linear mixed modeling approach to cyclic, spatial, and environmental drivers

This study presents a transferable linear mixed modeling framework to dissect cyclic, spatial, and environmental drivers of nitrous oxide (N2O) in a free stall dairy barn. Herein, concentrations in a barn were monitored over 10 days using photoacoustic spectroscopy across three spatial locations, vertical heights, and operational cycles. Linear mixed models were developed from simple to complex structures: starting with main effects (M-series: environmental drivers only), adding cycle-augmented terms (MC-series: environmental + cycle terms), and finally incorporating cycle-interaction dynamics (MIC series). The models evaluated cyclic, spatial, and environmental drivers for N2O concentration. Four environmental variables: temperature, relative humidity (RH), wind speed, and temperature–humidity index (THI) were analyzed for their impact on N2O concentrations. Twelve model variants were compared to identify the best fit. Our multi-criteria selection strategy identified MIC1 as optimal for prediction, with the lowest Akaike and Bayesian Information Criterion (AIC = 165,662; BIC = 165,785.6), root mean square error (RMSE = 33.9) and significant improvement in likelihood ratio tests (p < 0.001) over previous models. MC1 was selected for causal inference due to its robust coefficients (max VIF = 1.56) and comparable accuracy (RMSE = 34.2). While models using the THI underperformed, those with separate temperature and RH terms revealed dynamic cycle-phase interactions. RH exclusion severely degraded model performance. Temperature and RH synergistically amplified concentrations, with MIC1 showing a cycle 3 baseline elevation of 62.4 ppb and MC1 showing 68.8 ppb, while reversing temperature and RH effects. Spatial heterogeneity dominated while the vertical variation was minimal.