The data table used for the exploratory graphs and data analysis is shown with the first rows in Table 1. Julian Days represent the day of GHG collection. Block represents field replications, with a total of 3 blocks. Treatment represents the treatments in number, while TreatmentID has the specification of each treatment class. cumulative_CO2_flux_day and cumulative_N2O_flux_day are the calculated flux for CO2 and N2O, respectively, in daily basis.

The boxplot of CO2 flux (Figure 5) displays seasonal CO2 flux for each treatment over three years. 

Comparing the years, we can see that there is a trend of decreasing CO2 emissions over time. Further analysis is required to confirm whether this trend is statistically significant.

Comparing the treatments, we can observe a variability in the boxplots, likely due to the small sample size resulting from the block design (three repetitions per year). As boxplots do not directly assess normality, no assumption of normality was tested using Figure 5. Additionally, no single boxplot stands out from the rest, suggesting that we will see small effects of the treatments after the statistical analysis is completed. In other words, the treatments may not have had a great impact on GHG emissions, for either reducing or increasing the emissions, but further analysis must be conducted to identify which treatment had better outcomes.

The assumption of normality and homogeneity was done using histogram of residuals and residuals vs. fitted plot in Figure 6 for CO2 flux.

Figure 6: Histogram of residuals of CO2 flux (left) and Residuals vs. Fitted Plot (right). Data approximates a normal distribution.

The distribution of seasonal CO2 flux combined all treatments and years. As observed on Figure 6 (left) the data has a slight positive skew and on Figure 6 (right), the distribution is centered in the zero line and has a slight inhomogeneity observed by a few points being more scattered. However, the slight skewness and inhomogeneity are not strong enough to compromise the analysis and the assumption of normality and homogeneity. Based on these plots, no data transformation is necessary for the CO2 flux analysis.

The boxplot of seasonal N₂O flux per treatment per year is represented in Figure 7. In 2024, we can observe negative seasonal N2O flux, which can happen for a number of reasons such as plants taking N2O, microbes taking nitrogen from the air (as N2O) instead of from the soil, and error during sampling. More specifically in 2024, the crop used is a legume, fava beans, which are known for its ability to take up nitrogen from the atmosphere.

In 2022 and 2023, the boxplots show considerable variability, with long tails likely resulting from the small sample size of three repetitions per year. Although two treatments show higher values in 2023, the overlapping tails suggest that no single treatment clearly stands out as distinct from the others. 

The assumptions of normality and homogeneity were assessed using the histogram of residuals and the residuals vs. fitted plot shown in Figure 8. 

Figure 8: Histogram of residuals of N2O flux (left) and Residuals vs. Fitted Plot (right). Data has a positively skewed distribution.

The distribution of seasonal N₂O flux, combining all treatments and years, indicates that the data are not normally distributed. In the histogram (Figure 8, left), a positive skew is evident, with a long tail on the right side. In the residuals vs. fitted plot (Figure 8, right), the residuals are centered around the zero line but show a slightly greater spread on the positive side of the graph. Data transformation is necessary for the seasonal N2O flux analysis using a logarithmic transformation, with the resulting distribution shown in Figure 9.

After the logarithmic transformation, the differences between treatments remain minimal, with the boxplots overlapping one another (Figure 10). Seasonal N₂O flux values are still considerably smaller in 2024, supporting the earlier assumption that N₂O uptake by the crop may have occurred. Overall, the treatments do not appear to have had a substantial impact on N₂O emissions, but further statistical analysis is required to confirm whether any significant differences exist.