To explore the intrinsic spatial patterns of N 2 O emissions in agricultural systems, not only should the spatial and temporal variability in N 2 O emissions be analyzed separately, but the joint spatio-temporal variability should also be explored by applying spatio-temporal semivariogram models and interpolation methods. In this study, we ex- The N 2 O flux data were then log-transformed for normality. After detrending the influences from the chamber placement positions (Position) and the precipitation accumulated over two days (Rain2), the log-transformed N 2 O fluxes (FLUX30t) exhibited 15 strong spatial, temporal and joint spatio-temporal autocorrelations, which were used as three components of spatio-temporal semivariogram models and were characterized by models based on Stein's parameterized Matérn (Ste) function, exponential function and again the Ste function, respectively. The spatio-temporal experimental semivariogram of the N 2 O fluxes was fitted using four spatio-temporal semivariogram models 20(separable, product-sum, metric and sum-metric). The sum-metric model performed the best and provided meaningful effective ranges of spatial and temporal dependence, i.e., 0.41 m and 5.4 days, respectively. Four spatio-temporal regression-kriging interpolations were applied to estimate the spatio-temporal distribution of N 2 O emissions over the study area. The cross-validation results indicated that the four interpolations 25 % higher than the results predicted using the observations of large static chambers. Furthermore, compared with the other three models, the metric model exhibited weak sensitivity for peak prediction, although the cross-validation results indicated that they had same prediction capabilities. Our findings suggested: (i) that the size of large 5 static chambers used for long-term observations of N 2 O fluxes should be no less than 0.4 m and the time interval for gas sampling should be constrained to approximately 5 days; and (ii) that more efficient testing methods should be adopted to replace the conventional cross-validation methods for evaluating the performance of spatio-temporal kriging.

1. Spatio-temporal interpolations of the daily N 2 O fluxes (mgN m -2 d -1 ) obtained using the separable (Figure S1), product-sum ( Figure S2), metric ( Figure S3) and sum-metric ( Figure S4) models to fit semivariograms in spatio-temporal regression-kriging, respectively. 2.Spatial-temporal distributions of kriging standard deviations of the predicted N 2 O fluxes obtained using the separable (Figure S5), product-sum (Figure S6), metric ( Figure S7) and sum-metric ( Figure S8) models to fit semivariograms in spatio-temporal regression-kriging, respectively.