*2.4. Auxiliary Measurements*

Daily air temperature, atmospheric pressure and rainfall were recorded from the closest weather station (less than 500 m).

Soil temperature and volumetric water content were measured close to each collar simultaneously with the measurement of GHG fluxes from soil, using a dielectric probe (Decagon Devices GS3) inserted into the soil at a depth of 5 cm and linked to the instrument via Bluetooth ® connection. Soil water content values were used to calculate the soil water filled pore space (WFPS) according to Equations (1) and (2).

$$\text{Total porosity} \left( \% \right) = \frac{1 - \text{bulk density}}{2.65} \times 100 \tag{1}$$

$$\text{WFFPS} \left( \% \right) = \frac{\text{volumetric water content}}{\text{total porosity}} \times 100 \tag{2}$$

In Equation (1), bulk density was measured using the soil core method and particle density was considered equal to 2.65 g cm<sup>−</sup>3.

Soil samples were collected from the 0–20 cm soil layer for the determination of nitrate content (N–NO3) in each plot. Three soil cores per plot were mixed to constitute one sample. The samples were stored at 4 ◦C before their analysis. Before the analysis, each soil sample was dried at 40 ◦C until constant weight and then it was sieved at 2 mm. A 10 g subsample of soil was extracted using deionised water in 1:2.5 ratio and then it was shacked for 120 min. N–NO3 concentrations were determined using ionic chromatograph. Soil N–NO3 content was calculated based on N sample concentration considering soil dry weight.

#### *2.5. Data Elaboration and Statistical Analysis*

Data elaboration and statistical analysis were performed with R software [29], considering α = 0.05 as the passable level of significance.

N2O, CH4 and CO2 measurements were checked for outliers among replicates in each sampling day, through the Grubbs test. After outlier removal, N2O data were log transformed, as residuals deviated strongly from normal distribution. To enable this log-transformation, given the presence of negative values for daily N2O fluxes, N2O fluxes were translated before transformation as: (*<sup>N</sup>*2*<sup>O</sup> flux* + 0.1) − *min* (*<sup>N</sup>*2*<sup>O</sup> flux*), where *min* (*<sup>N</sup>*2*<sup>O</sup> flux*) was the minimum value in the dataset.

One-way ANOVA was used to analyse the e ffect of the factor "system" in each sampling date and separately for the two fields on: GHG daily fluxes, soil temperature, soil WFPS and soil nitrate concentration along the overall monitoring campaign.

The e ffect of the systems on average daily fluxes was analysed in the two periods (P1 and P2) and for the two fields separately, through linear mixed e ffect models, one for each gas, using the R "lme4" package [30]. The two fields were analysed separately because each phase of the crop rotation did not occur simultaneously in the two fields, since the first crops in summer 2014 were fennel in F1 and cabbage in F2.

The system was considered as a fixed factor of the linear mixed e ffect models, with the replicate as a random e ffect. When the system had a significant e ffect on the studied variable, Tukey's HSD post hoc test ( α= 0.05) was used to reveal the di fferences between the levels of the factor system.

The relationships among soil temperatures WFPS, N2O, CH4 and CO2 were analysed through the Spearman's correlation using the data collected across the overall field campaign and pooling the data of the two fields. Furthermore, the relationship between N2O daily flux and soil nitrate concentration was evaluated through the Spearman's correlation, considering the monitoring days in which the soil samples were collected. The relationship between CO2 emissions and soil temperature was evaluated to be exponential by plotting the data. Consequently, the analysis of covariance (ANCOVA) was used to compare the relationships between the logarithm of CO2 flux and the soil temperature in the three levels of the factor "system".

Cumulative emissions of N2O, CH4 and CO2, for both P1 and P2 were calculated by linear interpolation between two close sampling dates and the numerical integration of the function over time, assuming that fluxes changed linearly among sampling days. The e ffects of the system on the

cumulative emissions were analysed through linear mixed effect models, which were built for each gas in the same way as for the daily fluxes.

The overall GHG budget (CO2 equivalents) was calculated multiplying the cumulative value of each gas per period and field by the corresponding global warming potential (GWP) of AR5 [31]. The CO2 equivalents (CO2-eq) were calculated (i) separately for the non-CO2 gases, as the sum of cumulative emissions of N2O and CH4, and (ii) as the net GHG emissions, also considering CO2 emissions.
